If `z^4+1=sqrt(3)i` (A) `z^3` is purely real (B) z represents the vertices of a square of side `2^(1/4)` (C) `z^9` is purely imaginary (D) z represents the vertices of a square of side `2^(3/4)`

If (z - 1)/(z + 1) is purely imaginary, then |z| is

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

Which of the following is true for z=(3+2isintheta)(1-2sintheta)w h e r ei=sqrt(-1) ? (a) z is purely real for theta=npi+-pi/3,n in Z (b)z is purely imaginary for theta=npi+-pi/2,n in Z (c) z is purely real for theta=npi,n in Z (d) none of these

If (2z_1)/(3z_2) is purely imaginary then |(z_(1)-z_(2))/(z_(1)+z_(2))|

Let the complex numbers z_(1),z_(2),z_(3)" and "z_(4) denote the vertices of a square taken in order. If z_(1)=3+4i" and "z_(3)=5+6i , then the other two vertices z_(2)" and "z_(4) are respectively

If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary number.

Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alphaepsilonR then alpha is equal to (A) 2 (B) 1 (C) sqrt2 (D) sqrt3